Peak-to-average power ratio (PAR) reduction based on active-set tone reservation

ABSTRACT

In an embodiment, a transmitter includes first and second processing blocks, which may each include hardware, software, or a combination of hardware and software. The first processing block is operable to generate a first peak-reducing vector. And the a second first processing block is operable to receive a first data vector, the data vector comprising a plurality of samples, the first data vector having a first peak with a first index and a first magnitude, a second peak with a second index and a second magnitude that is less than the first magnitude, and a first peak-to-average power ratio, and to generate a second data vector having a second peak-to-average power ratio that is lower than the first peak-to-average power ratio by using the first peak-reducing vector.

PRIORITY CLAIM

The instant application claims priority to Chinese Patent ApplicationNo. 200910265275.7, filed Dec. 28, 2009, which application isincorporated herein by reference in its entirety.

BACKGROUND

Multicarrier transmission has been widely adopted in both wired andwireless communication systems such as asymmetric digital subscriberline (ADSL) systems, Digital Video Broadcast (DVB), and wirelesslocal/metropolitan area networks (WLAN/WMAN). Exploiting DiscreteMultitone Modulation (DMT) or Orthogonal Frequency Division Multiplexing(OFDM), these systems may achieve greater immunity to multipath fadingand impulse noise with lower cost. However, they may also suffer fromhigh peak-to-average power ratios (PAR). Without an appropriate processto counter this problem, the high PAR of a transmitted signal may causea high-power amplifier (HPA) to operate in its nonlinear region (i.e.,the peak-to-peak amplitude of the transmitted signal may be high enoughto saturate the amplifier), leading to significant performancedegradation.

OFDM effectively partitions overall system bandwidth into a number oforthogonal frequency subchannels. These subchannels are alsointerchangeably referred to throughout as “tones” or “subcarriers.” Inan OFDM system, an input serial data symbol is separated into D groups.Each of the D groups may be mapped onto a quadrature amplitude modulated(QAM) constellation point, and then modulated onto a respective one of Nsubchannels (or tones) having approximately equal bandwidth and afrequency separation of approximately 1/T, where T is the time durationof an OFDM symbol during which all N groups are transmitted, and D≦N.Generally, the larger the value of D, the larger the system bandwidth,and, because of a resulting quasi-Gaussian distribution in the resultingtime-domain signal, the higher the PAR (for example, peak amplitude toaverage amplitude).

Tone reservation, which modulates reserved or unused ones of the N toneswithin the signal space to produce data-block-dependent peak-cancelingsignals, is a technique for reducing the PAR for these systems. That is,where D<N, one may modulate one or more of the unused ones of the Ntones to reduce the PAR of the transmitted signal.

SUMMARY

A challenge in tone reservation is how best to produce thatpeak-canceling signal. Unfortunately, known solutions have typicallyinvolved high computational overhead, inaccuracy, or both.

According to an embodiment, a transmitter includes first and secondprocessing blocks, which may each include hardware, software, or acombination of hardware and software. The first processing block isoperable to generate a first peak-reducing vector. And the a secondfirst processing block is operable to receive a first data vector, thedata vector comprising a plurality of samples, the first data vectorhaving a first peak with a first index and a first magnitude, a secondpeak with a second index and a second magnitude that is less than thefirst magnitude, and a first peak-to-average power ratio, and togenerate a second data vector having a second peak-to-average powerratio that is lower than the first peak-to-average power ratio by usingthe first peak-reducing vector.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the subject matter disclosed herein will become morereadily appreciated as the same become better understood by reference tothe following detailed description, when taken in conjunction with theaccompanying drawings.

FIG. 1 illustrates an embodiment of an iterative method for PARreduction using a peak-canceling vector.

FIG. 2 is a flowchart of the embodiment of the iterative method for PARreduction depicted in FIG. 1.

FIG. 3 is a plot of an example time-domain waveform that may begenerated for the purpose of PAR reduction using reserved OFDM tones.

FIG. 4 is a plot of an example time-domain waveform that may beappropriate for PAR reduction using reserved OFDM tones.

FIG. 5 is a plot of an example time-domain waveform that may result fromusing a single iteration of an embodiment of a PAR reduction method.

FIG. 6 is a plot of an example time-domain waveform that may result fromusing a second iteration of an embodiment of a PAR reduction method.

DETAILED DESCRIPTION

The following discussion is presented to enable a person skilled in theart to make and use the subject matter disclosed herein. The generalprinciples described herein may be applied to embodiments andapplications other than those detailed above without departing from thespirit and scope of the subject matter disclosed herein. This disclosureis not intended to be limited to the embodiments shown, but is to beaccorded the widest scope consistent with the principles and featuresdisclosed or suggested herein.

In the following description, certain details are set forth inconjunction with the described embodiments to provide a sufficientunderstanding of the subject matter disclosed herein. One skilled in theart will appreciate, however, that the disclosed subject matter may bepracticed without these particular details. Furthermore, one skilled inthe art will appreciate that various modifications, equivalents, andcombinations of the disclosed embodiments and components of suchembodiments are within the scope of the disclosed subject matter.Embodiments including fewer than all the components or steps of any ofthe respective described embodiments may also be within the scope of thedisclosed subject matter although not expressly described in detailbelow. Finally, the operation of well-known components and/or processeshas not been shown or described in detail below to avoid unnecessarilyobscuring the disclosed subject matter.

FIG. 1 illustrates an embodiment of an iterative method for PARreduction using a peak-canceling vector. A time-domain data vector x(t),labeled x₀ for notational convenience, is the result of performing anInverse Discrete Fourier Transform (IDFT) with an oversampling factor Lon a frequency-domain OFDM symbol X that includes N information blocksX₀ . . . X_(N−1) respectively modulated on N subcarriers, plus D PARreduction blocks P₀ . . . P_(D−1) respectively modulated on Dsubcarriers, where D≦(L−1)N. A time-domain peak-canceling vector p₀,discussed in further detail below, is generated by performing an IDFT ona series of frequency impulses (ones) at one or more of the D reservedtones. An example of a peak-canceling vector p₀ is shown in FIG. 3.

If the PAR of the data vector x⁰ is above a target threshold, then afirst peak reduction is performed on the data vector x⁰ by locating thesample n₁ of x⁰ that has the greatest magnitude within the data vector;circularly shifting the peak-canceling vector p₀ by that number ofsamples n₁ to get a shifted peak-canceling vector p_(n1); scaling p_(n1)by a step size −μ₁ ¹ and complex coefficient α₁ ¹; and combining (e.g.,summing) the original data vector x⁰ with the shifted and scaledpeak-canceling vector p_(n1) to get a PAR-reduced data vector x¹. Inthis manner, in the vector x¹, the magnitude of the sample at n₁ isreduced to the magnitude of the sample at n₂ such that the magnitudes ofn₁ and n₂ are substantially equal and are the greatest peak magnitudesof x¹. The step size μ is a real quantity, used to modify the magnitudeof the vector p_(n1). The complex coefficient α is a complex coefficientvector used to modify both the magnitude and phase of the data vectorp_(n1), because the peak at n₁ of x⁰ has a phase as well as a magnitude,and so both the phase and magnitude of p_(n1) are scaled so as to givethe desired peak reduction at n1. Both μ and α are discussed in greaterdetail below.

In an embodiment, if the PAR of the data vector x¹ is above the targetthreshold, then a second peak reduction is performed on x₁ in a similarfashion. For this second iteration of peak reduction, the originalpeak-canceling vector p₀ is shifted by that number of samples n₂ toachieve a shifted peak-canceling vector p_(n2). Both μ and α areregenerated. The shifted vector p_(n2) is scaled by a step size −μ₂ ²and a complex coefficient α₂ ²; the shifted vector p_(n1) is scaled by astep size −μ₁ ² and a complex coefficient α₁ ². The complex coefficientsα cause the samples n₁ and n₂ of the combined shifted and scaledpeak-canceling vectors p_(n1) and p_(n2) to each have an appropriatemagnitude and the same phase (positive or negative) as the samples n₁and n₂ of x¹. The data vector x¹ is combined with these shifted andscaled peak-canceling vectors p_(n1) and p_(n2) to achieve thePAR-reduced data vector x². The real coefficients μ are used to reducethe magnitudes of x¹'s samples at n₁ and n₂ to substantially equal thatof the sample at n₃ of x². These three peaks (located at samples n₁, n₂and n₃) will have approximately the same magnitude value, which is thegreatest magnitude value in x².

In an embodiment, individual peak cancellation is reiterated byrepeating the above technique until the PAR of the resulting vector xequals or is less than the target threshold. In another embodiment, amaximum number of iterations number may be set even if the PAR of theresulting vector x is not less than the target threshold.

The time-domain waveform x(t) is the result of performing an IDFT on afrequency-domain OFDM symbol X, where the symbol X comprises Ninformation blocks modulated on respective N subcarriers. For complexbaseband OFDM systems, this time-domain waveform may be represented as:

$\begin{matrix}{{{x(t)} = {\frac{1}{\sqrt{N}}{\sum\limits_{n = 0}^{N - 1}\;{X_{n} \cdot {\mathbb{e}}^{{j2\pi}\; n\;\Delta\;{ft}}}}}},{0 \leq t \leq {N\; T}}} & (1)\end{matrix}$where X_(n), {n=0, 1, . . . , N−1} is the data symbol modulated onto thenth subchannel, Δf=1/NT is the subcarrier spacing, T is the timeduration of the OFDM symbol.

The PAR of this transmitted waveform x(t) is defined as:

$\begin{matrix}{{P\; A\; R} = \frac{\max\limits_{0 \leq t < {N\; T}}{{x(t)}}^{2}}{{1/N}\;{T \cdot {\int_{0}^{N\; T}{{{x(t)}}^{2}\ {\mathbb{d}t}}}}}} & (2)\end{matrix}$

To use tone reservation, the LN subcarriers (wherein L is theoversampling factor) in the OFDM system are divided into two subsets: asubcarrier set U for useful data (the tones N are in the set U) and asubcarrier set U^(c) for D≦(L−1)N PAR reduction blocks selected toreduce the PAR. As an example, in an embodiment wherein the signal spacecomprises a total of LN=256 subcarriers, one might reserve for PARreduction a set U^(c) of D=11 of those subcarriers with indexes k=[5,25, 54, 102, 125, 131, 147, 200, 204, 209, 247]. Expressing the sampledx(t) waveform as a sampled data vector x, one may also express a desiredpeak-cancelling waveform as a sampled vector c. The time-domain outputof the transmitter x is the sum of the data vector x and peak-cancelingvector c, which is given by:x=x+c=IDFT(X+C)  (3)Note that frequency-domain vector X=[X₀, X₁, . . . , X_(N−1)] is onlymodulated over subcarriers N within the data-carrying subset U;likewise, frequency-domain vector C=[C₀, C₁, . . . , C_(N−1)] is onlymodulated over subcarriers D within the reserved-tone subset U^(c). Thevectors X and C cannot both be nonzero on a given subcarrier; that is, asubcarrier may be a member of U or of U^(c), but cannot be a member ofboth U and U^(c):

$\begin{matrix}{{X_{k} + C_{k}} = \left\{ \begin{matrix}{X_{k},{k \in U}} \\{C_{k},{k \in U^{c}}}\end{matrix} \right.} & (4)\end{matrix}$C, therefore, is selected to reduce or minimize the PAR of thetime-domain output signal x by way of its time-domain correlation c:

$\begin{matrix}{{P\; A\; R} = \frac{\max\limits_{0 \leq k \leq {{NL} - 1}}{{{x\lbrack k\rbrack} + {c\lbrack k\rbrack}}}^{2}}{E\left\{ {{x\lbrack k\rbrack}}^{2} \right\}}} & (5)\end{matrix}$The calculation of a suitable vector for the time-domain vector c,without high computational overhead, may therefore result in PARreduction for an OFDM system.

FIG. 2 illustrates an embodiment of a method for calculating apeak-cancelling vector to achieve PAR reduction. As described above withrespect to FIG. 1, PAR reduction is performed iteratively, with aseparate stage for cancellation of each successive peak in thetime-domain data vector x, until a PAR threshold (or iterationthreshold) is reached. A first peak of greatest magnitude within datavector x is found and reduced using a shifted peak-canceling vectorscaled by real and complex coefficients until it is of substantiallyequal magnitude with another peak, e.g., the peak with the next greatestmagnitude. With a combined peak-canceling vector which has unitmagnitude and the phase of the reduced data vector at the locations ofthe two peaks, those peaks are reduced by an equal amount such that theythen have a magnitude substantially equal to that of a third peak havingthe third greatest magnitude, and so on. In an embodiment, individualpeak cancellation is reiterated until a target value for PAR isachieved. In another embodiment, a maximum iteration number M may bedesignated.

Starting in step 205, an N-subcarrier frequency symbol X={X₀, X₁, . . ., X_(N−1)} is converted into a first time-domain sampled data vector x⁰using an Inverse Discrete Fourier Transform (IDFT) with L-timesoversampling. A second L-oversampled vector p₀, termed thepeak-reduction kernel, may be computed in such a way as to provide atime-domain impulse at sample number n=0 with the D reserved toneswithin set U^(c). That is, to form the vector p₀, the D reserved tones(the D subcarriers within set U^(c)) are set to “1+j0, all other tonesin the subcarrier space (the N subcarriers within set U) are set to“0+j0”, and an IDFT is performed to achieve the time-domainpeak-reduction vector p₀, which is then normalized/scaled so that thevector p₀ has a maximum magnitude of 1 at the sample location n=0. Thephases of the D reserved tones are adjusted such that ideally, p₀ has apeak of highest magnitude at n=0, and the magnitudes of the peaks at allthe other sample locations are significantly lower (e.g., zero) than thepeak at n=0. But because the set U^(c) has a finite set of D tones, atleast some of the peaks at the other sample locations n≠0 may havenon-zero magnitudes.

In step 210, the first peak in data vector x₀ is determined such thatthe sample at that peak has the greatest magnitude in the vector. Let aniteration index i=1, and let E⁰ be the maximum magnitude in x₀. Further,let sample n₁ be the location where E⁰ is found. This sample n₁ is thelocation of the first peak within vector x₀ to be partially cancelled(i.e., reduced) to achieve PAR reduction. Also at step 210, this firstpeak is used to establish an active set of peaks A. At this point, theactive set A contains only the first peak at sample location n₁.

In step 215, a first complex coefficient α₁ ¹ is determined. Coefficientα₁ ¹ is the complex ratio between the complex value of x₀ at samplelocation n₁ and the maximum magnitude E⁰, such that

$\begin{matrix}{p^{1} = {{\alpha_{1}^{1}p_{n_{1}}} = {\frac{x_{n_{1}}^{0}}{E^{0}}p_{n_{1}}}}} & (8)\end{matrix}$where p_(n) ₁ is obtained by circularly shifting peak-reduction kernelvector p₀ by n₁ samples, and χ_(n1) ⁰ is the complex value of the samplen₁ Only α₁ ¹ and p¹ are determined with equation (8); successiveiterations, wherein the more generalized p^(i) is calculated, arediscussed below.

At step 220, peak testing is performed to locate samples in x_(i−1)(which, for the first peak, is x₀) which are not yet in the active set Athat possess large magnitudes relative to the other samples. Thesesamples are candidates for peak balancing in the next step, and areplaced in a test set B. For the very first peak reduction, active set Acontains only the one peak at n₁. Because it is possible for multiplepeaks to have the same magnitude, however, it is possible that multiplepeaks may be added to active set A in a single iteration. In oneembodiment, the magnitude of these samples may be approximated by simplytaking the sum of the absolute values of a given sample's real andimaginary components. In still another embodiment, peak testing may beskipped entirely. However, if peak testing is skipped, then the test setB will include all samples not in active set A, which greatly increasesthe computational load necessary for the next step 225.

In step 225, the minimum step size μ^(i) is determined as the differencein magnitude between the maximum magnitude of current data vectorx^(i−1) and that of the next iteration x_(i), such thatE^(i)=E^(i−1)−μ^(i), and μ^(i)=E^(i−1)−E^(i). This minimum step sizeμ^(i) may also be found according to the following equation:

$\begin{matrix}{\mu^{i} = {\min\limits_{q \in B}\left( {\frac{b_{q} - \sqrt{b_{q}^{2} - {a_{q}c_{q}}}}{a_{q}} \geq 0} \right)}} & (9)\end{matrix}$where a_(q)=1−p_(q) ^(i)(p_(q) ^(i))*, b_(q)=E^(i−1)−

(x_(q) ^(i−1)(p_(q) ^(i))*), c_(q)=(E^(i−1))²−x_(q) ^(i−1)(x_(q)^(i−1))*. The complex conjugate of any variable a is denoted by a*, and

(·) denotes the real part of a complex number. In embodiments whereinstep 220 (peak testing) was skipped, the determination of minimum stepsize μ^(i) may be more computationally intensive because test set B willbe much larger. In either case, the peaks within x^(i−1) having thecomplex magnitude associated with μ^(i) are then added to active set A.

At this point, if the iteration index i=1 (i.e., we are in the processof reducing the magnitude of the first peak), then we have alreadycalculated the complex coefficient α₁ ¹ in step 215 and we can proceedto step 235 to calculate the next iteration of data vector x_(i).

In step 230, the complex coefficients α are determined. As stated above,these complex coefficients are used both to scale the magnitude of therelevant peaks and to adjust the phase of those peaks such that at thelocations within active set A the combined peak-reduction vector p^(i)has unit magnitude and the same phase as the corresponding samples inx_(i−1). To solve for the α coefficients, the following complex matrixequation is used:

$\begin{matrix}{{\begin{bmatrix}1 & p_{n_{1} - n_{2}} & \cdots & p_{n_{1} - n_{i}} \\p_{n_{2} - n_{1}} & 1 & \cdots & p_{n_{2} - n_{i}} \\\vdots & \; & \; & \vdots \\p_{n_{i} - n_{1}} & p_{n_{i} - n_{1}} & \cdots & 1\end{bmatrix}\begin{bmatrix}\alpha_{1}^{i} \\\alpha_{2}^{i} \\\vdots \\\alpha_{i}^{i}\end{bmatrix}} = \begin{bmatrix}S_{n_{1}} \\S_{n_{2}} \\\vdots \\S_{n_{i}}\end{bmatrix}} & (10)\end{matrix}$Where p_(n) is the nth entry of p₀, andS _(n) _(l) =x _(n) _(l) ^(i−1) /E ^(i−1)  (11)All of the coefficients α are recalculated during each iteration, withthe leftmost matrix of equation (10) gaining another row and column eachtime. In an embodiment, this i×i system of complex matrix equations maybe replaced with a 2i×2i system of real equations. This and othersimplification techniques are discussed in “An Active-Set Approach forOFDM PAR Reduction via Tone Reservation”, Brian S. Krongold and DouglasL. Jones, IEEE Transactions on Signal Processing, Vol. 52, No. 2, pp.495-509, February 2004, the contents of which article are incorporatedherein by reference.

Once the coefficients [α₁ ^(i), α₂ ^(i), . . . , α_(i) ^(i)] arecalculated in step 230, then:p ^(i)=Σ_(i=1) ^(i)α_(l) ^(i) p _(n) _(l)   (12)

The iterative data vector x^(i) is determined by adding p^(i),negatively scaled by the minimum step size μ^(i), to the prior iterativevector x^(i−1), so that:x _(i) =x _(i−1)−μ^(i) p ^(i)  (13)This has the result of reducing the magnitudes of a number, e.g., i,peaks in the active set by the magnitude of μ^(i).

The iteration index i is incremented such that i=i+1. If neither themaximum number of iterations nor the desired PAR value has beenachieved, then the next iteration of peak reduction is begun byreturning to step 220 for peak testing (or, in embodiments where peaktesting is skipped, step 225 for directly finding the minimum stepsize).

If the desired PAR or maximum iterations M have been achieved, then theoutput x is equal to current data vector x^(i).

Returning to FIG. 1, in the leftmost stage 101, a first Inverse DiscreteFourier Transform (IDFT) block 110 provides an LN-point oversampledtime-domain vector x for each frequency block X={X₀, X₁, . . . ,X_(N−1)}. Also in stage 201, a second IDFT block 120 calculates anLN-point oversampled vector p₀. This vector p₀ may be computed in such away as to provide a time-domain impulse at sample number n=0 with the Dreserved tones within set U^(c), and scaling p₀ such that it possesses avalue of 1 at the location n=0. Frequency-domain impulses occur forevery reserved tone D in the set, so that P={P₀, P₁, . . . , P_(N−1)}.In one embodiment, these reserved tones are unchanging, so that the samefrequency domain vector P may be used for all blocks X. In otherembodiments, the reserved tones may vary depending on the value of X,such that P (and, therefore, p) are recalculated for each block X.

Stage 102 illustrates the first iteration of peak reduction. A firstpeak within data vector x₀, having the maximum magnitude E⁰, is locatedat sample n₁ and added to an active peak set A (not shown). Reductionkernel vector p₀ is circularly shifted by that sample number n₁ so thatthe highest amplitude in p₀, formerly located at n=0, is now aligned atn=n₁. Test set B is achieved by peak testing to find those samples whichare not yet in the active set A and possess large magnitudes relative tothe other samples in x₀. Using equation (9), for example, this allowsthe determination of the minimum step size μ¹, which is the differencein magnitude between the first peak, with magnitude E⁰, and the peakwith the second-greatest complex magnitude in x₀.

The first complex coefficient α₁ ¹ is then determined, p¹ is found as α₁¹ p_(n) ₁ , and c¹ is found as p_(n) ₁ (−μ¹α₁ ¹). By scaling p_(n) ₁ bythe complex coefficient α₁ ¹, p¹ has the same phase as that of x₀ at n₁.By scaling p¹ by the negative step size −μ¹, the magnitude of the peakat n₁ is reduced to substantially match that of the next peak or peaksto be reduced. This is reflected in the resulting vector x¹, whichpossesses both the peak located at sample n₁ as well as the secondarypeak located at n=n₂ when determining the minimum step size μ¹—but inthe data vector x¹, each of those peaks possess substantially the samemagnitude.

In stage 103, the process is repeated with iteration index i=2. Here,two peaks are being reduced: the first peak located at n₁, and anothersecondary peak located at n₂. The minimum step size μ² may be foundusing equation (9) based on the peaks of data vector x₁ within the testset B; complex coefficients α₁ ² and α₂ ² are determined using equation(10); and the peak-reduction vector c₂ is found as −μ²p²=p_(n) ₁ (−μ²α₁²)+p_(n) ₂ (−μ²α₂ ²). The subsequent data vector is thus found asx₂=x₁+c₂. The coefficients α₁ ² and α₂ ² are calculated so that even ifp_(n) ₁ has a nonzero magnitude at sample n₂, the magnitude of thereduced peak at n₂ still substantially equals the magnitude of the peakat n₃, and even if p_(n) ₂ has a nonzero magnitude at sample n₁, themagnitude of the reduced peak at n₁ still substantially equals themagnitude of the peak at n₃.

Stage 104 illustrates the Mth iteration of an embodiment of the peakreduction method. A total of M peaks are being reduced in complexmagnitude simultaneously, with the first M−1 peaks already having beenreduced by previous iterations. The output data vector is x=x+c, where xis the original data vector given by IDFT(X) and c is the time-domainsum of c₁+c₂+ . . . +c_(M).

Referring again to FIG. 1, an embodiment of the above-described PARreduction technique is described with less emphasis on the mathematicsand more emphasis on the physical phenomena.

Referring to block 101, an IDFT of an OFDM data signal is generated, andan IDFT of an OFDM peak-reduction kernel is generated. The OFDM datasignal includes subcarriers that are selected for data transmission, andthe OFDM peak-reduction kernel includes subcarriers that are not usedfor data transmission (e.g., because of excessive channel interference,distortion at the frequencies of these non-data subcarriers, or a desireto reserve those subcarriers for purposes of PAR reduction). The firstIDFT yields a time-domain data signal x₀ having a duration equal to asymbol period, and the second IDFT yields a time-domain peak-reductionpulse p₀ also having a duration of one symbol period. An example of p₀is plotted in FIG. 3. The first and second IDFTs may be performed by aprocessor or other circuitry in a transmitter.

Referring to block 102, the transmitter identifies the peaks of x₀having the greatest magnitude and the second greatest magnitude as beinglocated at sample locations n₁ and n₂, respectively.

Then, the transmitter circularly shifts p₀ to generate a peak-reductionpulse p_(n1) having its main peak at sample location n₁.

Next, the transmitter generates −μ¹ having a value such that when addedto the magnitude of x₀ at sample location n₁, −μ¹α₁ ¹p_(n1) causes themagnitude of the peak of x₁ at sample n₁ to equal, or approximatelyequal, the magnitude of the peak of x₀ at sample n₂, as shown in block103. The transmitter then adds −μ¹α₁ ¹p_(n1) to x₀ to obtain thetime-domain waveform x₁ in block 103.

Then, referring to block 103, the transmitter identifies the peaks of x₁at sample locations n₁ and n₂ as having the greatest magnitude, andidentifies the peak of x₁ at n₃ as having the second greatest magnitude.

Next, the transmitter circularly shifts p₀ to generate a peak-reductionpulse p_(n1) having its main peak at sample location n₁, and alsocircularly shifts p₀ to generate a peak-reduction pulse p_(n2) havingits main peak at sample location n₂.

Then, the transmitter generates −μ² having a value such that when addedto the magnitude of x¹ at sample location n₁, −μ²α₁ ²p_(n1) causes themagnitude of the peak of x₂ at sample n₁ to equal, or approximatelyequal, the magnitude of the peak of x₁ at sample n₃. Furthermore, thetransmitter generates α₁ ² and α₂ ² such that the magnitude of x₂ atsample location n₂ is approximately equal to the magnitude of x₁ at thesample location n₃ even if the magnitude of p_(n1) at sample location n₂is nonzero.

Because the magnitudes of x₁ at sample locations n₁ and n₂ aresubstantially equal to one another, when added to the magnitude of x₁ atsample location n₂, −μ²α₂ ²p_(n2) causes the magnitude of the peak of x₂at sample n₂ to equal, or approximately equal, the magnitude of the peakof x₁ at sample n₃. Furthermore, the transmitter generates as α₁ ² andα₂ ² such that the magnitude of x₂ at sample location n₁ isapproximately equal to the magnitude of x₁ at the sample location n₃even if the magnitude of p_(n2) at sample location n₁ is nonzero.

The transmitter then adds −μ² α₁ ² p_(n1) and −μ² α₂ ² p_(n2) to x₁ toobtain the time-domain waveform x₂, which is output from the block 104.

Referring to block 104, the transmitter continues in this manner for M−3additional peaks until it generates a time-domain data signal x_(M)having no peaks larger than a selected peak threshold, or until M equalsa selected iteration threshold.

FIG. 3 is a plot of an example of a time-domain peak-reduction waveformp₀ that may be generated for the purpose of PAR reduction using reservedOFDM tones. In the embodiment depicted, the kernel p₀ is generated usingD=11 reserved tones in a signal space having a total of LN=256subcarriers. As discussed above, the kernel may have, therefore, beengenerated using a 256-point IDFT. One can see that the kernel p₀ has itsgreatest peak of approximately unity (normalized) magnitude at samplen₀.

FIG. 4 is a time-domain magnitude plot of a complex-baseband OFDM signalusing the same system parameters as in the embodiment depicted in FIG.3. Again, the signal space comprises 256 subcarriers, 11 of which arereserved for the purpose of PAR reduction. In the waveform depicted byFIG. 4, the highest peak may be seen as occurring in the area of sampleindex n₁₅₀. The waveform has a PAR of 10.45 dB.

FIG. 5 is a magnitude plot of the complex-baseband OFDM signal from FIG.4 after a single iteration of the PAR reduction method described aboveusing the peak-reduction kernel p₀ depicted in FIG. 3. As a result ofthat single iteration, the PAR of the signal has been reduced toapproximately 7.56 dB. In the depiction of FIG. 5, the peak locatedapproximately at sample index n₁₅₀ has been reduced in magnitude toapproximate that of a second peak, located in the region around sampleindex n₇.

FIG. 6 is a magnitude plot of the complex-baseband OFDM signal from FIG.3 after two successive iterations of the PAR reduction method describedabove using the peak-reduction kernel p₀ depicted in FIG. 3. As a resultof these two successive iterations, the PAR of the signal has beenreduced to 6.92 dB. In the depiction of FIG. 6, the peaks locatedapproximately at sample indexes n₁₅₀ and n₇, respectively, have beenreduced in magnitude to approximate that of a third peak, located in thearea around sample index n₂₃₈.

It is to be understood that even though various embodiments andadvantages have been set forth in the foregoing description, the abovedisclosure is illustrative only, and changes may be made in detail, andyet remain within the broad principles of the disclosed subject matter.For example, the method and system may be implemented in either softwareor hardware embodiments, and may comprise one or more integrated circuitdevices. In some embodiments, the methods or individual steps describedmay be performed in a hardware implementation. In other embodiments, asoftware implementation may be utilized. In still other embodiments, themethods or individual steps described may be performed by a combinationof hardware and software modules. Furthermore, p₀ may have its mainpulse at any sample location other than n₀. Moreover, there may be othertechniques for generating p₀.

What is claimed is:
 1. A transmitter, comprising: a first processingblock configured to generate a first peak-reducing vector; and a secondprocessing block configured: to receive a first data vector, the datavector comprising a plurality of samples, the first data vector having afirst peak with a first index and a first magnitude, a second peak witha second index and a second magnitude that is less than the firstmagnitude, and a first peak-to-average power ratio, and to generate asecond data vector having a second peak-to-average power ratio that islower than the first peak-to-average power ratio by using the firstpeak-reducing vector; wherein generating the second data vectorincludes: generating a second peak-reducing vector by shifting the firstpeak-reducing vector by a number of samples substantially equal to thefirst index; generating a third peak-reducing vector by scaling thesecond peak-reducing vector by a first coefficient, and by furtherscaling the second peak-reducing vector by a second coefficient; andgenerating the second data vector by combining the third peak-reducingvector with the first data vector; and at least one of the firstprocessing block and second processing block is implemented by hardware.2. The transmitter of claim 1, wherein the first coefficient comprises acomplex coefficient.
 3. The communications system of claim 1, whereinthe second coefficient comprises a real coefficient.
 4. A method forreducing peak-to-average-power ratio (PAR) in a signal, the methodcomprising: receiving a first data vector, the data vector comprising aplurality of samples, the first data vector having a first peak with afirst index and a first magnitude, a second peak with a second index anda second magnitude that is less than the first magnitude, and a firstpeak-to-average power ratio; generating a first peak-reducing vector;and using the first peak-reducing vector to generate from the first datavector a second data vector having a second peak-to-average power ratiothat is lower than the first peak-to-average power ratio whereinreducing the magnitude of the first peak includes: shifting thepeak-reducing vector by a number of samples substantially equal to thefirst index; generating a second peak-reducing vector by scaling thefirst peak-reducing vector by a first factor substantially equal to thedifference between the first and second magnitudes, and by furtherscaling the first peak-reducing vector by a second complex factor; andgenerating a second data vector by subtracting the second peak-reducingvector from the first data vector.